Are the following pairs of statements are negation of each other.

(i) The number x is not a rational number.

The number x is not an irrational number.

(ii) The number x is not a rational number.

The number x is an irrational number.

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Solution

(i) The number x is not a rational number.

$\Rightarrow$ The number x is an irrrational number.

$∴$ The statement "The number x is not an irrational number". is a negation of the first statement.

(ii) The number x is not a rational number.

$\Rightarrow$ The number x is an irrational number.

$∴$ The statement "The number x is an irrational number". is not a negation of the first statement.

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